1TH/vwo §6.4 Formulas from graphs 1st Form (short version)

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

§6.4 Making a FORMULA from a GRAPH

For this graph...

... we cannot make a formula, sadly enough.

A STRAIGHT LINE = our type of graph!

Look at the following slide. For this Graph we CAN

make a Formula!  Reason to be happy!

Example 1

For wat kind of Graph CAN we make a Formula ?

1. a graph that goes up and down
2. a linear graph
3. a graph that has the form of a circle
4. a straight line, that is not vertical

Example 1

You will LEARN how to

make a FORMULA for

a graph like this!

First I show you the

general METHOD. 

Maybe this Theory doen't explain much to you...

That's  why a few EXAMPLES follow.

One about a RISING GRAPH and one about a 

FALLING GRAPH.   

Example 2: As you see, we have a falling graph here.

Let's call the horizontal axis a and the vertical axis b.

Step 1.   Above you see the table with 3 points from the graph.

Let's call the horizontal axis a and the vertical one b.

Step 2.  The graph starts at height 5 on the vertical axis. So that's the starting value.

Step 3.  When the graph goes to the right 1 step, it goes down 2 steps.

Step 4.   Putting steps 2 and 3 in the shape of a Formula:   

                 a x -2 + 5 = b         or         also:            b = -2 x a + 5 

Let us Study the Theory one more time!

            

a	0	1	2
b	5	3	1

Slides 14 t/m 19 we skip for now.

TASK:

Make a FORMULA for the GRAPH on the next slide.

Get a pen, pencil and geo and open your Notebook.

Use the METHOD you just saw.    Two TIPS:

1st        Forgotten all about it?

              It's on p.216 in your Textbook!

2nd      The number that you calculate in step 3 this time is a FRACTION!  

              Apparently Charlie Brown and Lucie are not impressed.  I hope YOU are!   

To make this task more interesting ....

Let's make it a FOTOVRAAG!                

So 

* make it

* take a picture and

* send this in in Lessonup!

This is MY SOLUTION, take it or leave it.

step 1.Above you see the Table, 

that contains 3 points from the graph.

Let's call the axes:         a and b.

step 2.  The starting value is 5, because at that height the

                graph starts at the vertical axis.

step 3. Now the amount the graph goes down per step of 1 for x:

                 If you go 3 steps to the right, then you go down 2 steps.  So:

                If you go 1 step     to the right, then you go down       of a step.

step 4.  The Formula becomes:  b = 5 -       x a

               

            

x	0	3	6
y	5	3	1

​3​​2​​

​3​​2​​

The + and - signs make a huge difference:

PRACTICE PRACTICE PRACTICE ...

Now it's time you make a FORMULA for a GRAPH yourself!

FOTOVRAAG- to be handed in, in the next slide!

- have you got your:

   1. Notebook   2. pencil   3. geo  4. eraser    before you?

- if not, get it right now!

- the task starts; 

   1. make it in your Notebook   2. take a pic   3. send it in in!

Use the Method from p.218 

again!

FOTOVRAAG

28a - my work on Andrews' Formula:

Solution:

Homework time.

You may skip 25 and 26

Make §6.4 now.   Don't forget to:

+  check your work with the Solutionsbook